Articles in PresS. J Neurophysiol (July 8, 2015). doi:10.1152/jn.00217.2015
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Generalization and transfer of
contextual cues in motor learning
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Abbreviated title: Contextual generalization in motor learning
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A.M.E. Sarwary1, 2, D. F. Stegeman2, L.P.J. Selen1, W.P. Medendorp1
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Radboud University Nijmegen, Donders Institute for Brain, Cognition and
Behaviour, The Netherlands
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Radboud University Medical Centre Nijmegen, Department of Neurology, Donders
Institute for Brain, Cognition and Behaviour, The Netherlands
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Corresponding author:
Adjmal M.E. Sarwary
Donders Institute for Brain, Cognition and Behaviour
Centre for Cognition
P.O. Box 9104, NL-6500 HE, Nijmegen
The Netherlands
Phone: +31 24 361 2542
FAX: +31 24 361 6066
Email: [email protected]
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Number of pages: 42
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Number of figures: 5
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Number of tables: 1
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Number of words: Abstract (246), Introduction (603), Discussion (2121)
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Financial interests or conflicts of interests (if applicable): none
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Acknowledgements:
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This work was supported by an internal grant from the Donders Centre for
Neuroscience and by the European Research Council (EU-ERC-283567), EUFP7-FET grant (SpaceCog 600785), and the Netherlands Organization for
Scientific Research (NWO-VICI: 453-11-001 & NWO-VENI: 451-10-017). We
thank Bas van Lith for assistance with data collection.
Copyright © 2015 by the American Physiological Society.
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Abstract
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We continuously adapt our movements in daily life, forming new
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internal models whenever necessary and updating existing ones. Recent work
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has suggested that this flexibility is enabled via sensorimotor cues, serving to
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access the correct internal model whenever necessary and keeping new
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models apart from previous ones. While research to date has mainly focused
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on identifying the nature of such cue representations, here we investigated
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whether and how these cue representations generalize, interfere, and transfer
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within and across effector systems. Subjects were trained to make two-stage
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reaching movements: a pre-movement that served as a cue, followed by a
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targeted movement that was perturbed by one of two opposite curl force
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fields. The direction of the pre-movement was uniquely coupled to the
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direction of the ensuing force field, enabling simultaneous learning of the two
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respective internal models. After training, generalization of the two pre-
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movement cues’ representations was tested at untrained pre-movement
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directions, both within the trained and untrained hand. We show that the
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individual pre-movement representations generalize in a Gaussian like pattern
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around the trained pre-movement direction. When the force fields are of
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unequal strengths, the cue-dependent generalization skews toward the
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strongest field. Furthermore, generalization patterns transfer to the non-
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trained hand, in an extrinsic reference frame. We conclude that contextual
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cues do not serve as discrete switches between multiple internal models.
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Instead, their generalization suggests a weighted contribution of the
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associated internal models based on the angular separation from the trained
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cues to the net motor output.
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Keywords: motor adaptation; contextual cues; generalization; interlimb
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transfer
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Introduction
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of our body and environment by building and adjusting internal models,
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thought to be formed by changes to motor primitives (Thoroughman and
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Shadmehr, 2000; Donchin et al., 2003; Poggio and Bizzi, 2004). These
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changes cause that an internal model for reaching, acquired at a specific
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movement direction, not only guides movements in that direction but also
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generalizes to neighboring movements (Mattar and Ostry, 2010; Izawa et al.,
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2012). The extent of this generalization reduces as a function of the angular
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separation from the trained movement direction.
Our brain is able to adapt our movements to changes in the dynamics
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If multiple internal models are learned for the same movement direction
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the same set of motor primitives will be involved in the adaptation. This
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typically causes interference between representations, slowing down or even
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abolishing learning of the internal models (Caithness et al., 2004).
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Contextual cues are known to reduce this interference. Multiple internal
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models can be learned and recalled in parallel if each of them is uniquely
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linked to a contextual cue, like wrist posture (Gandolfo et al., 1996), a
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visuomotor association (Hirashima and Nozaki, 2012), a pre-movement
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(Howard et al., 2012), or vestibular input (Sarwary et al., 2013).
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If multiple internal models can be learned based on contextual cues,
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how does the brain generalize across these cue representations (‘cues’ for
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short)? Analogous to the generalization of an internal model around the
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trained movement direction, cue-related internal models could also show
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generalization around the trained cue dimension. If so, one would predict that
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in a paradigm where two distinct contextual cues are linked to two distinct
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internal models, the net generalization represents the combined effect of the
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two single cues’ generalization profiles. In support, Ghahramani & Wolpert
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(1997) reported that when subjects learn two starting-point dependent
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visuomotor mappings, the generalization of this learning to untrained starting
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points can be described by a mixture of the two learned maps. The first
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objective of this study is to test cue-based generalization in human subjects
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adapting their reaches to two opposite curl force fields each associated with
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their own contextual pre-movement cue (Howard et al., 2012).
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An internal model acquired for reaching with one hand does not only
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generalize within that hand, but also generalizes to the untrained hand. This
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transfer is only about 10% (Joiner et al., 2013), with ongoing debate on
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whether it takes place in extrinsic (Dizio and Lackner, 1995; Criscimagna-
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Hemminger et al., 2003) or intrinsic coordinates (Wang and Sainburg, 2004;
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Galea et al., 2007). Following from this notion, our second objective is to test
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whether and if so, in which reference frame, the cue-related generalization
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transfers to the un-trained hand.
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Our subjects made two-stage reaching movements (Fig. 1): The first
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movement served as a contextual cue for the perturbing forces in the second
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movement (Howard et al., 2012). Two pre-movement directions were uniquely
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coupled
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generalization around the trained pre-movement directions and transfer of this
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generalization pattern to the untrained hand. In a second experiment we
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focused on interference between the two cue-related internal models by
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changing the relative strength of the associated force fields. In a third
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experiment we determined the generalization pattern around a single
with
opposite
force fields. After
adaptation,
we
quantified
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association between a pre-movement cue and force field.
We show that generalization of the contextual pre-movement cue follows
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Gaussian-like
decay
around
the
trained
direction.
Individual
cue
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generalizations interfere at intermediate directions, as revealed by a mixed
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expression of the two associated internal models. Furthermore, cue-related
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generalization transfers to the untrained hand in an extrinsic frame of
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reference, irrespective of whether learning was performed with the dominant
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or non-dominant hand.
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Materials and Methods
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Participants
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Experiments were conducted under the general approval for behavioral
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experiments by the institutional ethics committee. In total 40 (30 female) naive
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subjects between 18 and 28 years of age (mean = 23.4, SD = 3.0) gave their
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written consent to participate in the experiments. Reimbursement was
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provided in terms of payment. All subjects had normal, or corrected-to-normal
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vision and had no known motor deficits. All subjects were right-hand dominant
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with a laterality index of 100 according to the Edinburgh test of handedness
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(Oldfield, 1971).
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Apparatus and setup
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Subjects were seated on a height adjustable chair in front of a robotic rig (Fig
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1A). Both their right and left arm rested on air sleds floating on a glass top
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table. Reaches were performed while holding the handle of a planar robotic
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manipulandum, vBot (Howard et al., 2009). The vBot in combination with the
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air sled only allows movement in the horizontal plane and measures position
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and generates forces at the handle that are updated at 1000 Hz. Stimuli were
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presented within the plane of movement via a semi-silvered mirror, reflecting
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the display of a LCD monitor suspended horizontally above (Fig. 1A). This
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configuration also allowed visual feedback of hand position to be overlaid into
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the plane of the movement. Subjects were prevented from viewing their arm
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directly. Start position, via-point, and target position were presented as circles
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of 1.5 cm radius. Current hand position was represented by a red circle of 0.5
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cm radius.
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Reach task
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Subjects had to perform reaching movements consisting of two stages. The
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first stage was an unperturbed contextual pre-movement (10 cm amplitude)
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from the start position to the via-point. The second stage was a target-directed
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movement from the via-point to the target position (12 cm amplitude). At the
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beginning of a trial, start position (in grey), via-point (in yellow) and target
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position (in yellow) were simultaneously displayed.
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Contextual pre-movement: Before the start of a trial the subject had to place
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the hand cursor within the start position and stay still (cursor speed < 5cm/s
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for 100msec). Then, a tone instructed to start the contextual pre-movement
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reach. If the reach was initiated before the tone or started >1s after the tone,
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an error message appeared on the screen (‘wait for beep’ or ‘move after
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beep’) and the trial was repeated. If the pre-movement ceased at the via-point
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with a speed < 5cm/s, the via-point turned green and a second tone signaled
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to continue the reach towards the target. If subjects did not stop their
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movement at the via-point, or the pre-movement had a duration > 500msec,
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an error message was displayed on the screen (‘stop at via-point’ or ‘move
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faster’) and the trial was repeated. During the pre-movement stage of the
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reach the vBot’s motors were always turned off.
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Targeted movement: The start of the targeted movement was defined as the
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first point where the hand speed was > 5 cm/s after the second tone. If
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subjects did not initiate the targeted movement within 400msec after the
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second tone, an error message was given (‘move after second beep’) and the
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trial was repeated. The endpoint of the targeted movement was defined as the
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first point where the speed < 5cm/s. If this endpoint was within the target
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position, the target turned from yellow to green. If the endpoint was not within
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the target position a feedback message was given (‘stop at target’). If the
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endpoint was within the target position, but the movement duration was >
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500msec a ‘move faster’ feedback message was given. These feedback
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messages were used to make the reaches more consistent, but did not lead
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to rejection of the trial.
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During the targeted movement the motors could be off (null), produce a curl
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force field (clockwise or counterclockwise) or produce an error clamp (Scheidt
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et al., 2000; Smith et al., 2006).
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A curl force field produces forces that are perpendicular to movement
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direction and proportional to the reach velocity:
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(1)
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in which the damping constant b was set to +13 and -13 Ns/m (equal strength
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CW and CCW force fields), or to +16 and -8 Ns/m (unequal strength CW and
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CCW force fields, respectively). The sign of b thus determined the direction of
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the force field (CW or CCW) and was uniquely coupled to a contextual pre-
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movement direction.
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Error-clamp trials constrain the movement onto a straight line from the start to
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the target position. The hand was constrained to a straight path using a spring
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constant of 6,000 N/m and a damping constant of 7.5 Ns/m. Both the curl
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force fields and error clamps were initiated at the onset of the second tone,
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from which damping and spring constants were linearly ramped up over 50
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msec to avoid instabilities due to discontinuities in the forces.
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Experiment 1: equal strength force fields
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Two groups of 8 subjects performed the reach task. One group learned to
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compensate for the cued force fields with their dominant (i.e. right) hand and
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the other group learned this with their non-dominant (i.e. left) hand. Start
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positions for the pre-movements were defined on a 10 cm radius circle
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centered around the via-point. A total of 14 pre-movement directions (-135, -
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95, -65, -45, -30, -15, 0, 15, 30, 45, 65, 95, 135, 180 degree) were defined on
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this circle (Fig 1B). Only the -45º and 45º pre-movement directions were
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linked to a force field in the subsequent targeted movement. This 12cm
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targeted movement was always in the mid-sagittal plane, for both the right
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and left hand.
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Subjects started an experimental session using the untrained hand.
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With this hand they performed 182 null trials (13 batches of the 14 pre-
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movement cues) to get accustomed to the passive robot dynamics and the
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experimental constraints. In each batch the 14 pre-movement cues were
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presented in random order. Within these 13 batches, each pre-movement
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direction was randomly probed 5 times with an error-clamp to assess baseline
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force expression during the targeted movement.
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The same 182 null trials were repeated with the opposite hand, i.e. the
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hand that would subsequently learn the associations between the two pre-
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movement cues and force fields.
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After having established the baseline performance for each hand, a
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block of 400 adaptation trials followed (group 1: right hand; group 2: left
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hand), in which subjects learned the pre-movement cue to force field
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associations. The pre-movements were made from the -45º and 45º start
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positions (Fig 1B), which provided a unique cue to the force field of the
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subsequent targeted movement (-45º pre-movement cued the CW field; 45º
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pre-movement: cued the CCW field). The two pre-movement cues were
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presented pseudo randomly, such that a batch of 10 trials contained 4 CW
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trials, 4 CCW trials and 2 error-clamp trials, one for each pre-movement cue.
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The error clamp trials measured the degree of adaptation to each cued force
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field.
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Subsequently, the generalization of the force fields in relation to the
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two pre-movement cues was probed, by testing the force expression in the
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trained and untrained hand for all 14 pre-movement directions using error-
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clamps. Probe trials were mixed with re-exposure trials to keep adaptation at
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asymptotic level. Re-exposure trials were applied to the originally trained hand
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for the two trained pre-movement cues and their respective force fields (Fig
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1B). In each batch of 6 trials, the 3rd trial was an error clamp trial with the
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untrained hand, the 6th an error clamp trial with the trained hand, and the
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remaining four trials were re-exposure trials to the trained hand. A message in
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the workspace display indicated the hand switches. Both hands were
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supported by their own air sled and the subject only needed to change the
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hand that grasped the handle of the vBOT. All fourteen pre-movement
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directions were probed 5 times in each hand, resulting in a total of 420 trials
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(6 *14 * 5).
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Finally, the session ended with a wash-out block of 70 trials, entailing
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reaches with the trained hand in all possible pre-movement directions, each
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presented 5 times in random order.
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Experiment 2: unequal strength force fields
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In a second experiment we examined in further detail the interference
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between the two cue-related internal models. To this end, 8 new subjects
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performed our cued reaching task, but now the opposite force fields had
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unequal strengths. This experiment was similar to experiment 1, however we
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only trained and probed generalization of the dominant right hand. Subjects
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were exposed to one null block (182 trials), an adaptation block (400 trials), a
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probing block (140 trials) and a washout block (70 null trials). During the
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probing block all 14 cue angles (same as in experiment 1) were probed 5
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times. Re-exposure trials were mixed in with error-clamp trials such that every
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second trial was a re-exposure trial.
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Experiment 3: single pre-movement cue
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In a third experiment, we investigated whether the simultaneously observed
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generalization patterns of two cue representations relate to the generalization
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of a single cue after having learnt a single force field. We tested 16 right-hand
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subjects, divided in two groups, using right-hand reaching movements. One
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group (n=8) had the -45º pre-movement cue coupled with a clockwise force
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field; the other group had the 45º cue coupled to a counter clockwise force
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field (field strengths as in exp 1). Subjects were exposed to one null block
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(182 trials), an adaptation block (200 trials), a probing block (140 trials) and a
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washout block (70 null trials). All 14 cue angles (same as in experiment 1)
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were probed 5 times during the probing block. Every second trial of the
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probing block was a re-exposure trial.
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Analysis
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Data were stored for offline analysis in MATLAB (The MathWorks).
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Kinematics and dynamics of the targeted movement were the main focus of
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the analyses. For completeness, we also analyzed the kinematics of pre-
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movements to assure that kinematic differences between the cue movements
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cannot drive our effects.
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Start (t0) and endpoint (tf) of the targeted movement was determined
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based on a speed threshold of 5 cm/s. In all but the error clamp trials,
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deviation of the movement trajectory from a straight line was calculated using
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the signed hand-path error (E) defined as:
(2)
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where x(t) is the perpendicular distance of the actual trajectory compared to a
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straight line joining start position at the via-point and target position and ẏ(t) is
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the hand velocity in the direction of the target (Franklin et al. 2003).
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From the error-clamp trials, we computed an adaptation index (AI)
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representing the degree of force compensation to the curl-force field. For each
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trial, the theoretical time-varying force generated by the curl field was
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calculated based on actual hand velocity. This theoretical force was regressed
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against the force measured in the error-clamp, providing a regression
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coefficient in the range of -1 to 1 (Smith et al., 2006). The sign was introduced
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to separate the compensatory forces for the CW and CCW curl fields.
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Adaptation indices were baseline corrected by subtracting for each pre-
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movement direction the mean AI derived in the null trials, recorded in the
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beginning of the paradigm. In the analyses of experiment 2 we regressed the
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force expression against the theoretical forces of the strongest force field. As
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a result, perfect compensation for the weaker force field would result in an AI
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of 0.5.
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To assess learning during the adaptation block we looked at kinematic
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(E) and dynamic (AI) learning parameters. We used paired t-tests comparing
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the average of the initial 5 versus final 5 hand-path errors and the average of
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first 2 versus last 2 AI. To check whether adaptation levels remained at an
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asymptotic level during the generalization block, we performed ANOVAs with
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E or AI as dependent variables.
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Learning rates
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To quantify learning rate in the adaptation blocks, we fitted a single-rate
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exponential function to the pattern of the hand-path error:
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(3)
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in which E0+Ef represent the error at the first trial, τ the time constant (in trials)
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of adaptation and Ef the asymptote error, and n trial number. As two internal
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models (CW and CCW) were learned simultaneously, we flipped the sign of
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the 45º cue HPEs and collapsed the data of the opposite field before
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performing an exponential fit. We used confidence intervals assessed via
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bootstrapping (1000) to compare exponential fit values of dominant hand and
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non-dominant hand training.
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Generalization curves
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During the adaptation block, the two opposite force fields were trained
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simultaneously with -45º and 45º pre-movement cue directions. To infer the
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generalization around the pre-movement cues, we assumed the force
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expressed during the targeted movement, as measured by AI, to fall-off in a
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Gaussian fashion with angular deviation of the pre-movement from the trained
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direction. Because each cue is associated with its own internal model, the
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observed cue generalization curve was regarded as a net expression of two
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cue-based internal model representations. As a result, we modeled the
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generalization of the trained cues as two overlapping Gaussian shaped
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functions, both centered at their trained pre-movement direction (-45º and
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45º):
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(6)
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in which c represents pre-movement direction, with c-45 and c45 referring to the
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trained directions. The model contains 5 free parameters: two gain factors A-45
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and A45, that represent the force expression at the two trained cue angles, two
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width parameters σ-45 and σ45, that represent the angular extent of
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generalization around the trained cue angles, and an overall offset term B.
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This model was fit independently to the AI data from the trained and untrained
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hand. Statistical differences between model-parameters for the trained and
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untrained hand were assessed using t-tests.
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The model was then used to make predictions for the interference
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levels between internal models of unequal strength in experiment 2. These
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predictions were based on σ set to the combined average of σ-45 and σ45
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across all subjects obtained from experiment 1. The offset (B) parameter was
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set to 0, and the gain parameters A-45 and A45, stemmed from the behavioral
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data of experiment 2, by averaging the final 6 AIs of the -45 and 45 degree
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cue on an individual subject basis. We also fitted the model to the individual
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subjects’ data with 4 free parameters (A45, A-45, B and σ-45 = σ45) and then
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compared the fitted parameters to the parameters we used to make
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predictions using t-tests.
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Finally, a similar, but reduced model was used to fit the data of
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experiment 3, in which the generalization of a single cue in relation to a
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single-force field was investigated. Therefore, the model contained only a
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single Gaussian shaped function centered at the trained pre-movement
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direction in combination with an offset term.
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Results
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We performed three experiments. In the first experiment, subjects learned to
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compensate for two opposite force fields of equal strengths, each cued by a
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unique pre-movement direction (-45º or 45º). After learning we probed the
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spatial generalization of these pre-movement cues in the trained hand and
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their transfer to the untrained hand. In the second experiment, subjects also
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learned two cue-related (-45º and 45º) opposite force fields, but now of
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unequal strength. This should result in different interference levels of pre-
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movement cues. We used a cue-based generalization model to interpret
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generalization of both the equal and unequal strength force field
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representations. The validity of this model was further investigated in a third
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experiment in which we quantified generalization around a single cue in
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relation to a single-force field.
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We start with the description of the results of the first experiment in
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which one group trained with their dominant (right) hand and another group
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with their non-dominant (left) hand (Fig 1B). After both force fields had been
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learned, the force expression during the targeted movement was measured
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for untrained pre-movement directions, for both the trained and untrained
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hand (Fig 1C).
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Simultaneous learning of two internal models
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Both the dominant and non-dominant hand training group learned to
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compensate for the CW and CCW force field. Figures 2A and 2B show the
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evolution of the hand-path error over the adaptation and generalization phase
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of the experiment for training with the dominant and non-dominant hand,
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respectively. Both groups show adaptation to the two force fields, which was
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verified by a significant decrease in hand-path error from the first 5 to the last
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5 trials of the adaptation block (each p < 0.001). This observation was
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corroborated by a significant increase in AI, a measure of the compensatory
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force into the error clamps, over the course of the adaptation (first two versus
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last two trials; each p < 0.001) for both force fields and subject groups (Fig 2C
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and 2D).
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Figure 2 also suggests that the non-dominant hand is slower in
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learning to compensate for the force fields. To quantify this, we fitted a single
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rate exponential function to the hand-path error (see Methods). For this
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analysis we collapsed the data of the two cues (-45º and 45º) after changing
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the sign of the force expression from the 45º cue. The exponential function
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represents the speed of learning by the parameter τ. Comparing the τ values
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across groups based on 1000 bootstraps, the dominant hand (τ = 28.3 trials,
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95% CI [13.5 43.1]) learns significantly faster than the non-dominant hand (τ =
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76.7 trials, 95% CI [55.5 97.9]).
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The paradigm was designed such that the level of adaptation, as
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obtained at the end of the adaptation phase, should remain unchanged during
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the subsequent block that probes generalization. Figure 2 shows E and AI for
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the trained cue locations for the trained hand during the probing phase of the
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paradigm, which both remain virtually constant. To substantiate this
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observation, we performed a 3 way ANOVA on E and AI with the factors block
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(adaptation, probing), pre-movement direction (-45º, 45º) and hand (dominant,
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non-dominant). When comparing E averaged across the final 15 trials of the
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adaptation versus probing phase, there was no significant effect of block
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(F(1,57)=0.09; p=0.77), pre-movement direction (F(1,57) < 0.001; p=0.99), or
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hand (F(1,57)=0.03; p=0.87), or any of their interactions (each p > 0.26).
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Likewise, comparing AI (taking the mean of the final 2 trials of each phase),
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revealed no significant effects of block (F(1,57)=0.02; p=0.88), pre-movement
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direction (F(1,57)=0.15; p=0.7), or hand (F(1,57)=0.05; p=0.83), or their
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interactions (each p > 0.66). Together, this indicates that adaptation levels
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indeed remained unchanged during the probing phase, a prerequisite to be
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able
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representations.
to
probe
reliably
the
generalization
of
pre-movement
cue
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Generalization of pre-movement cue representations
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Our data hitherto show that two internal models of reach dynamics are formed
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simultaneously, each contextually associated with a distinct pre-movement
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cue (-45º or 45º). The next question is whether and how these pre-movement
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cue representations generalize to untrained pre-movement directions.
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Figure 3 shows the adaptation indices as determined during the error
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clamp trials of the probing phase, plotted as a function of pre-movement
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direction. Data are organized separately for the two groups (Fig 3A: training of
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dominant, right hand; Fig 3B, training of non-dominant, left hand). Both panels
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show clear generalization of context within the trained hand, i.e. the force
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expression during the targeted movement depends on the direction of the pre-
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movement. The fall-off in force expression, as measured by AI, seems
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steeper in between the two trained pre-movement directions (between -45º
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and 45º pre-movement directions) than for pre-movement directions outside
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this range (|direction|>45º). Furthermore, figure 3 illustrates that the
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generalization effects of the pre-movement representations, as seen in the
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trained hand, transfer to the untrained hand, irrespective of whether the
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dominant (right) or non-dominant (left) hand was trained. Next we will analyze
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these data in more detail, first for generalization in the trained hand and then
441
for transfer of this generalization to the untrained hand.
442
443
Generalization of context in the trained hand
444
To quantify the generalization results within the trained hand, we fitted two
445
superimposing Gaussians (see Methods), centered at -45º (blue) and 45º
446
(red) pre-movement directions, in terms of gain (A) and width (σ). The fitted
447
net generalization curves (black and green) are overlaid onto the data points,
448
yielding R2 values of 0.98 (p<0.001) for the dominant (black) and 0.97
449
(p<0.001) for the non-dominant hand (green), respectively. From the
450
underlying representations (blue and red), it can now be clearly seen that their
451
overlap explains the steep fall-off at the intermediate pre-movement direction
452
(≈ 0º).
453
The gain values (A-45 and A45) indicate the fraction of compensatory
454
force at the trained cue locations, which are comparable to the asymptotic AI
455
values at the end of learning. They are significantly different from zero (p <
456
0.001) for both the dominant hand (A-45 = 1.12, SE = 0.05; A45 = -0.92, SE =
457
0.05) and the non-dominant hand (A-45 = 1.06, SE = 0.08; A45 = -0.96, SE =
458
0.05).
459
The widths of the Gaussians, characterizing the generalization curve of
460
the cue representation, range from 39 to 57 degrees. The width of the
461
Gaussians, associated with the -45º and 45º cue, are not significantly different
462
(dominant: σ-45 = 40º, SE = 2º; σ45 = 47º, SE = 4º; p = 0.13; non-dominant: σ-
463
45
464
and σ45 for each subject before comparing the extent of cue generalization in
465
the dominant and non-dominant hand training groups. The non-dominant
466
hand shows a significantly (p = 0.01) broader generalization for a single pre-
467
movement cue (σnon-dominant = 51º, SE = 2º) than the dominant hand (σdominant =
468
43º, SE = 2º). This difference can also be observed in figure 3, comparing the
469
underlying representations (blue and red) across the trained hands (Fig 3A
470
versus 3B). The offset term B was not significantly different from zero (p =
471
0.07).
= 57º, SE = 5º; σ45 = 44º, SE = 4º; p = 0.12). Therefore, we collapsed σ-45
472
473
Context transfers to untrained hand
474
The next question to be addressed with experiment 1 was whether the
475
observed generalization pattern in the trained hand also transfers to the
476
untrained hand. Apart from the generalization within the trained hand, Figure
477
3 also shows the transfer of generalization of pre-movement cue
478
representations to the untrained hand. Using the same Gaussian mixture
479
modeling approach as for the trained hand, we quantified the force expression
480
in the non-trained hand. There is clear transfer from the trained dominant to
481
the untrained non-dominant hand as indicated by the force expression,
482
quantified by A, being significantly different from zero for both cues (A-45 =
483
0.11, SE = 0.03; A45 = -0.14, SE = 0.03; p-45 = 0.02, p45=0.002). Both cue
484
representations also show the same amount of transfer to the untrained hand
485
(~10%, p = 0.45). There is also significant transfer from the trained non-
486
dominant to the untrained dominant hand (A-45 = 0.13, SE = 0.02; A45 = -0.12,
487
SE = 0.02; p-45 = 0.001, p45 < 0.001). Again, the two cue representations are
488
similar in the amount of transfer (~10%) (p = 0.65).
489
The width of the fitted Gaussians for the -45º and 45º pre-movement
490
cues do not differ in the untrained hand. Neither in the dominant to non-
491
dominant hand transfer group (Fig 3A, σ-45 = 46º, SE = 13º; σ45 = 48º, SE =
492
9º; p = 0.9) nor the non-dominant to dominant hand transfer group (Fig 3B, σ-
493
45
494
significantly different from zero (p = 0.2).
= 66º, SE = 13º; σ45 = 59º, SE = 11º; p = 0.63). The offset B is also not
495
Finally, we asked in which reference frame this transfer took place. An
496
intrinsic reference frame would suggest that the pattern of cue generalization
497
of the trained hand is mirrored along the mid-sagittal plane, i.e. around the 0
498
degree direction, in the transfer to the untrained hand. Transfer in an extrinsic
499
reference frame would entail that the same, non-mirrored, pattern of
500
generalization would be observed in the untrained hand. Figure 3 clearly
501
indicates the latter, suggesting that transfer of the pre-movement cue
502
representations across hands occurs in an extrinsic reference frame.
503
504
Interference between contexts: force fields of unequal strength
505
Thus far, we showed that the pattern of generalization observed in experiment
506
1 is consistent with a model in which motor output is the weighted sum of
507
separate internal models of the CW and CCW fields. The contribution of each
508
internal model is weighted by a separate Gaussian function, which is tuned to
509
the direction of the contextual pre-movement. At intermediate pre-movement
510
directions this results in interference between representations. To further test
511
this model, we performed an additional experiment (experiment 2), testing
512
generalization and interference of cued internal models associated with
513
unequal field strengths (CW = 2*CCW). The prediction is that the increased
514
output from the internal model associated with the CW field should skew the
515
context-dependent pattern of generalization towards the CW cue direction.
516
Figure 4A shows that subjects can learn two force fields of unequal
517
strength based on pre-movement cues. The hand-path error
(Fig 4A)
518
demonstrates a significant decrease over the course of trials (both p<0.001),
519
which was complemented by a significant increase of the AI (both p<0.01). A
520
2-way ANOVA on E (averaged across the final 15 trials of each phase)
521
revealed no differences between adaptation and probing blocks (F(1,28)=4.25;
522
p=0.29), or between the two pre-movement directions (F(1,28) = 54.98; p=0.09).
523
The interaction between the two factors was also not significant (F(1,28)=0.03;
524
p=0.87). The 2-way ANOVA results of the AI (taking the mean of the final 2
525
trials of the adaptation and probing block), revealed no significant difference
526
between the adaptation and probing block (F(1,31)=18.95; p=0.14) either.
527
However, there was a significant effect of pre-movement direction
528
(F(1,31)=5936; p=0.008) on the magnitude of the AI, caused by the different
529
force field strengths. The interaction of block x pre-movement is not significant
530
(F(1,31)=0.004; p=0.95), confirming that adaptation levels remained constant
531
throughout the probing phase for both force fields.
532
The results from experiment 1 were interpreted in terms of a mixture of
533
two Gaussian shaped generalization curves. Based on the parameters of this
534
model we made predictions for experiment 2 based on Eq 6. The σ-45 and σ45
535
values, obtained independently in experiment 1, did not show a significant
536
difference and were therefore set to their combined average of σdominant (43º).
537
The offset parameter B of Eq 6 was set to 0 for each subject. Gain
538
parameters were derived from the individual subject data, taken as the
539
average of the final 6 AIs for each cue separately on an individual subject
540
basis.
541
In addition, we fitted the model from Eq 6 leaving all parameters free
542
(σ-45 = σ45, A45, A-45 and B) on an individual subject basis. Figure 4C shows
543
the model prediction (solid lines) and model fit (dotted black line) based on the
544
group average. The prediction (R2=0.95) and the model fit (R2=0.96) match
545
closely. Figure 4D shows the model predictions with data points (black circles)
546
for the individual subjects. The data points closely match with the prediction of
547
the model, with correlations that have R2 values > 0.84 (each p<0.001).
548
However, it is important to point out that our behavioral data represents
549
the net generalization output. The values of A-45 and A45 that we used to make
550
predictions were based on the net generalization output and do not
551
necessarily represent the true gain of the underlying cue generalization
552
curves. This explains why the model underestimates the net AI for the 45º cue
553
in figure 4C. We can also not rule out changes of σ and B in experiment 2.
554
Therefore we also fitted the 4 parameter model and compared the fitted
555
values to the values we used to make predictions.
556
The σ and B parameters are not significantly different between the
557
prediction and the model fits (pσ = 0.48, pB = 0.26). The A-45 gain also shows
558
no significant difference (p = 0.98). However, as expected from figure 4C, the
559
A45 values directly derived from the AIs are significantly different from those of
560
the model fits (p = 0.03). This confirms that the underlying representation of
561
the force field obtained at the 45º cue is stronger than suggested by the net
562
generalization curve. This can be explained by the interference of the stronger
563
representation for the -45º cue representation.
564
Further support for altered levels of interference between cues that
565
represent unequal strength force fields is provided by the angular shift of the
566
zero crossing of the AI. Based on the model, the zero AI crossing point is not
567
at 0º anymore (like in experiment 1), but is now shifted towards the 45º cue,
568
which represents the weaker force field. This is also confirmed in the AI data
569
where the AI amplitude of the -15º cue is significantly larger than the AI
570
amplitude of the +15º cue (p = 0.008, AI-15deg = 0.49, SE = 0.07 and AI15deg = -
571
0.17, SE = 0.04).
572
Taken together, the results from the prediction, model fit and raw data
573
further validate the cue-based weighted contribution of the two internal
574
models that we proposed in experiment 1.
575
576
Generalization of a single context in the trained hand
577
Experiments 1 and 2 involved two pre-movement cues associated with their
578
own force field, CW or CCW. Our model could describe the generalization
579
results assuming two independent, superimposing Gaussians. How valid is
580
this assumption? In a third experiment, using two groups of 8 subjects, we
581
investigated the generalization of a single cue representation (-45º or 45º)
582
after single-force field adaptation.
583
Figure 5A,B show that both groups adapted to the force field, indicated
584
by a significant decrease in hand-path error (both p < 0.01) and a significant
585
increase in AI (both p < 0.001). A 2-way ANOVA using E (averaged across
586
the final 15 trials of each phase) revealed no significant difference between
587
adaptation and probing blocks (F(1,28)=0.02; p=0.91), or between the trained
588
pre-movement directions (F(1,28)=0.13; p=0.78), or interaction (F(1,28)=1.92;
589
p=0.18). This is also supported by absence of change in AI (taking the mean
590
of the final 2 trials of the adaptation and probing block) for the factor of block
591
(F(1,28)=2.28; p=0.37), pre-movement direction (F(1,28)=0.31; p=0.68), and the
592
interaction (F(1,28)=0.79; p=0.38).
593
Our main question concerns the generalization around the trained pre-
594
movement cue. As figure 5C illustrates the generalization curve is composed
595
of a global (offset B) and a local Gaussian modulation. The overall offset,
596
captured by B, is about 0.4 (SE = 0.02). Furthermore, the local Gaussian
597
modulation had a gain (A) of about 0.46 (SE = 0.02) and a width of about
598
27.4º (SE = 1.9º), which is significantly smaller than the width estimated in
599
experiment 1 (p < 0.001).
600
601
602
Pre-movement kinematics cannot explain generalization
603
Howard et al. (2012) showed that dwell time, i.e. the time the hand stays in
604
the via-point, influences the expression of an internal model in the subsequent
605
targeted movement. Therefore we checked whether dwell time (the time that
606
the velocity remained below 5cm/s in the via-point) systematically varied with
607
respect to pre-movement direction. We also checked whether peak speed and
608
pre-movement duration (start and endpoint of the pre-movement were
609
determined based a 5cm/s speed threshold) systematically varied with pre-
610
movement direction. We performed 3 ANOVAs, one for each dependent
611
variable (dwell time, peak speed of pre-movement, pre-movement duration)
612
with the factors pre-movement angle, hand and trained hand. None of the
613
main factors was significant and can therefore not explain our results (table
614
1).
615
With respect to the interactions, the only consistent significant effect
616
across these three dependent variables is the Hand x Trained Hand
617
interaction. In other words, the right hand performed faster reaches when it
618
was the hand that had learned the force fields (trained hand). If the left hand
619
was trained, it performed the faster reaches. This all stems from the far
620
greater number of pre-movements made with the trained compared to the
621
non-trained hand (80% vs 20%).
622
623
Discussion
624
We studied the generalization of contextual pre-movement cues that enable
625
simultaneous learning of two opposite force environments. Our results show
626
that the force expression based on individual contextual cues follow a
627
Gaussian like pattern around the trained cue. For equal strength force fields
628
this results in a steep fall-off for cue angles between the two trained cues. For
629
unequal force field strengths this also results in skewing the pattern of
630
generalization toward the strongest field. We further find that these cue
631
related force expression transfer both from dominant to non-dominant hand
632
and vice-versa, in an extrinsic frame of reference. Finally, we show that the
633
generalization of the two simultaneously learnt cue representations cannot
634
simply be described as the combined generalization of single cue
635
representations after adaptation to a single force field.
636
637
Generalization of contextual cues
638
Our results confirm previous findings (Howard et al., 2012) that pre-movement
639
cues enable the acquisition of multiple motor memories at the same time. The
640
two cues that were used to provide context for two opposite force fields are
641
single instances from a continuum of possible pre-movement directions, here
642
across angular space. The novelty of our research is that we tested whether
643
and how these single cue instances generalize along the pre-movement
644
dimension.
645
We show that the amount of force expression reduces with angular
646
separation from the originally coupled cue. We quantified the spatial extent of
647
this generalization by fitting two Gaussian shaped functions to the AIs. The
648
estimated widths of the generalization functions show that the non-dominant
649
hand has a wider cue representation compared to the dominant hand.
650
Supporting evidence for a wider generalization pattern in the non-
651
dominant hand is also provided by a recent study that used bimanual
652
movements: reaches of one arm were perturbed and uniquely coupled to one
653
movement direction of the other arm (Yokoi et al., 2014). After training,
654
generalization was assessed by measuring force expression of the perturbed
655
arm using error clamps, for different movement direction of the unperturbed
656
arm. Their results also revealed a Gaussian like pattern of generalization,
657
which was wider when the dominant hand was perturbed compared to the
658
non-dominant hand. The authors attribute this finding to the perturbed hand,
659
arguing that the dominant hand shows wider generalization than the non-
660
dominant hand. However, we favor an alternative interpretation. The untrained
661
hand’s movement direction served as a contextual cue, implying that the
662
wider generalization is attributed to the non-dominant rather than the
663
dominant hand. What could account for this difference in representation
664
between the two hands?
665
One explanation is related to the encoding of the contextual cue
666
information. Contextual information derived from the pre-movement can be
667
derived from visual or proprioceptive signals. Visual input is equivalent for
668
both hands and can therefore not explain the difference in width. However,
669
proprioceptive signals are likely to differ: it has been shown that the
670
proprioceptive sense of the non-dominant is more variable than the dominant
671
hand in the central workspace (Wong et al., 2014). As a result, the non-
672
dominant hand’s cue information is more variable, which in turn explains a
673
wider generalization pattern.
674
In our first two experiments we estimated the generalization of
675
individual pre-movement cues based on a Gaussian model fit to the net
676
generalization pattern. In our third experiment we specifically tested the
677
generalization of single pre-movement cue after single force field adaptation.
678
This revealed a global and a local generalization component, which were both
679
different from generalization pattern in the first two experiments, which
680
showed no global component and wider local tuning. We showed that the sum
681
of the independently assessed curves (Fig 5C, dotted line) does not capture
682
the net generalization curve obtained in experiment 1. What can explain this
683
discrepancy?
684
A possible explanation may be found in the actual role of a contextual
685
cue. A contextual cue contains information that can successfully aid in
686
distinguishing one force environment from another. If there is only one such
687
environment, then a cue may be superfluous to the information provided by
688
the targeted movement through the force field. If the brain considers the cue
689
irrelevant, subjects will always show full expression of their internal model in
690
the targeted movement, irrespective of the pre-movement direction. However,
691
if the cue is part of the internal model, one could expect a Gaussian fall-off as
692
the direction of the cue-movement changes.
693
Our data show a mixture of both: the presence of a global component
694
and the narrower tuning of the local component indicate the qualitative
695
difference between the information represented by a single pre-movement
696
cue compared to the information represented if two pre-movement cues to
697
two opposite force fields are trained.
698
An alternative explanation may be that the number of pre-movement
699
cues changes their underlying representation. Support for this notion stems
700
from findings by (Thoroughman and Taylor, 2005), testing adaptation of
701
reaching movements to perturbing forces that changed directions at different
702
rates relative to the direction of movement. They reported that subjects
703
narrowed the spatial extent of generalization with increasing complexity of the
704
environmental dynamics. In the present case, the increase in complexity is not
705
related to the force fields perturbations but originates in the number of cue
706
related force fields learnt. This could explain why generalization is wider for
707
the single cue compared to the more complex, dual cue experiment. Further
708
support comes from a recent study in which the single cue was not an active
709
but a passively-induced pre-movement (Howard and Franklin, 2015). The
710
authors observed a global AI of 0.6, which is higher than the present AI of 0.4.
711
This larger extent of generalization suggests that the complexity of the
712
environment is lower with passive compared to active pre-movements.
713
714
Transfer of cue-related internal models
715
We also show that contextual pre-movement cues transfer to the untrained
716
hand in an extrinsic reference frame, consistent with findings of (Criscimagna-
717
Hemminger et al., 2003; Joiner et al., 2013). This suggests that the internal
718
model and its associated contextual cues share similar underlying
719
representations, although we do not want to claim that a single reference
720
frame is involved. Indeed, recent work has demonstrated that generalization
721
takes place in a mixture of many reference frames (Berniker et al., 2013). In
722
this light, our paradigm only unveiled the net result of multiple underlying
723
reference frames, which appeared to be the extrinsic reference frame.
724
The present results also speak to the debate about the direction of
725
transfer. Some studies have suggested that internal models are transferred
726
from the dominant to the non-dominant hand, but not vice versa (Sainburg,
727
2002; Criscimagna-Hemminger et al., 2003;). Our results clearly show transfer
728
in both directions, using a similar adaptation task. What could give rise to this
729
discrepancy?
730
Studies that showed an asymmetry of transfer across hands used the
731
learning rate as an indicator of transfer (Sainburg, 2002; Criscimagna-
732
Hemminger et al., 2003;). In these studies, one hand is first exposed to a
733
force field block and subsequently the opposite hand (learning rate paradigm).
734
If transfer of learning between hands occurs, the subsequent opposite hand
735
should be faster in learning compared to naïve, which is what they found for
736
the non-dominant but not for the dominant hand. In our paradigm we
737
assessed transfer by using error-clamp trials, thereby avoiding any exposure
738
of the untrained hand to the force field. Using this way of testing, we found
739
that about 10% of the learned internal model transferred to the untrained
740
hand, irrespective of hand dominance. We suggest that this difference in
741
transfer can be explained by how it is tested.
742
If one tests transfer based on increased learning rate, there are two
743
possible ways of how transfer could be revealed: First, learning of the
744
opposite hand could start from a reduced initial kinematic error, caused by the
745
10% compensatory force transferred from the trained hand, but with the
746
learning rate itself untouched. However, 10% compensatory force is small,
747
and could easily go unnoticed if not specifically tested using error clamps as
748
we did here.
749
Second, initial errors might start from the same level as naïve, but the
750
reduction of these errors, i.e. learning rate, is ramped up. It was recently
751
shown that the history of errors influences the learning rate (Herzfeld et al.,
752
2014). This means that if errors are experienced during testing of transfer, as
753
in a learning rate based transfer paradigm, the learning rate itself can be
754
influenced by previously experienced errors. However, because we used error
755
clamps, our subjects never experienced any errors while testing transfer. This
756
line of reasoning would suggest that, in a learning rate paradigm, past errors
757
from the trained hand are incorporated differently with respect to transfer – i.e.
758
they are incorporated in dominant hand learning and ignored in non-dominant
759
hand learning. How could this be explained?
760
One possibility could be that the uncertainty of the observed errors is
761
part of the internal representation of past errors. In force field learning one
762
source of error is detected through proprioception. Proprioception of the
763
dominant hand is known to be more precise than of the non-dominant hand
764
(Wong et al., 2014). As a result, the internal representation of past errors from
765
the dominant hand may be more precise than that of the non-dominant hand.
766
This difference in precision may explain why the internal model of errors of the
767
non-dominant hand has little effect on the learning rate of the dominant hand.
768
Conversely, the non-dominant hand benefits from the more precise internal
769
representation of past errors of the dominant hand, increasing the learning
770
rate of the non-dominant hand.
771
Alternatively the difference in learning rate paradigms can also be
772
explained by the suggestion that dominant and non-dominant hand respond
773
different to errors (Shabbott and Sainburg, 2008). This could explain why
774
learning rate studies only reported unidirectional transfer, while our study
775
based on error clamps shows a clear bi-directional transfer between hands.
776
777
Learning rate differences between the dominant and non-dominant hand
778
We show that the dominant hand is faster in learning cue-based
779
internal models compared to the non-dominant hand - most prominently seen
780
in error-clamp trials. One might argue that this difference in learning rate is
781
caused by differences in the specialization of the dominant and non-dominant
782
hand. The non-dominant hand may rely more on impedance control and
783
therefore shows less force in the channels, whereas the dominant hand may
784
rely more on feed forward force control (Sainburg, 2002). Alternatively, the
785
learning rate differences could be related to the wider generalization in the
786
non-dominant hand compared to the dominant hand. Internal models with
787
broader generalization curves show more interference, which would slow
788
down learning. This explanation is in line with Yokoi et al. (2014)’s finding of a
789
slower learning rate when the non-dominant hand codes for context, while the
790
dominant hand is exposed to multiple force fields.
791
792
Implications for models of sensorimotor learning
793
Several computational models of motor adaptation have been proposed in the
794
past. However, very few models contain a notion of context that would enable
795
learning of multiple internal models.
796
The Modular Selection and Identification for Control (MOSAIC) model,
797
proposed by Haruno et al. (2001), entails two parts within its architecture; one
798
part enables internal model selection prior to movement onset and the other
799
permits dynamic selection during movement execution. Lee and Schweighofer
800
(2009) proposed a two-state model containing a fast process (fast learning,
801
fast forgetting) and a slow process (slow learning, slow forgetting) arranged in
802
a parallel architecture to update the beliefs about the perturbations. Their
803
model uses contextual cues to switch between the states associated with the
804
slow process. Thus, in both models, contextual cues serve as discrete
805
switches to select one of multiple internal models.
806
Only the modular decomposition model proposed by Ghahramani and
807
Wolpert (1997) contains a notion of cue-generalization, but lacks a notion of
808
the learning process. In their study, two unique start positions were coupled to
809
opposite visuomotor mappings. After training, generalization was tested at
810
untrained starting locations. The authors showed that a mixture of Gaussian
811
representations around the trained starting locations could explain the
812
observed pattern of generalization. The present results suggest that their
813
conclusions also apply to force field learning, even with cues that are not part
814
of the perturbed movement itself. In addition, the findings of our second
815
experiment, with unequal force field strengths, show that the mixture
816
proportion of the two internal models is preserved along the pre-movement
817
dimension (i.e. the generalization width remains the same), but that the
818
difference in peak force of the internal models results in a behavioral shift of
819
the generalization curve.
820
In conclusion, we show that two cue-related internal models are
821
weighted along the cue dimension, modulating a single internal model’s
822
contribution to the net motor output. In addition, we show that the untrained
823
hand has access to this representation of internal models and cues in an
824
extrinsic reference frame.
825
826
827
828
829
830
831
832
833
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Figure Table/Legends
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917
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919
A: Setup: Subjects were seated in front of a robotic rig performing reaches
holding the handle of a planar robotic manipulandum (vBot). Both arms were
resting on air sleds floating on a glass top table. Courtesy of Franklin and
Wolpert, 2008.
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B: Task: Reaches were performed starting with a pre-movement from start
position to via-point. This was followed by a movement from via-point to
target. The three panels show the pre-movement directions and perturbation
couplings used within the null, training, and probing block.
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925
C: Paradigm. Illustration of the force field schedule within each block. Vertical
grey bars denote error-clamp trials.
Figure 1. Experimental design.
926
927
928
929
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931
Figure 2. Hand-path error (left panels) and Adaptation Index (right panels)
during adaptation and probing phases of the paradigm, averaged across
subjects. Shaded areas denote SE. Top row, dominant hand trained, bottom
row, non-dominant hand trained. Blue: clockwise force field (CW). Red:
counterclockwise force field (CCW).
932
933
Figure 3. Adaptation Index as a function of pre-movement direction.
934
A: Dominant hand training to non-dominant hand transfer.
935
936
937
938
939
B: Non-dominant hand training to dominant hand transfer. Error bars denote
SE. Red and blue dots represent force field trained at pre-movement
directions. The Gaussian fits are superimposed: black (dominant hand), green
(non-dominant hand). The model-based generalization curves of the single
cues are plotted in blue and red, respectively.
940
941
Figure 4. Adaptation with unequal strength force fields.
942
943
A: Hand-path error of both force fields during adaptation and probing phase:
CW (blue), CCW (red).
944
B: Adaptation Index of both force fields during adaptation and probing phase.
945
946
947
C: Group average data, error bars denote SE. The model predictions are
superimposed: black (net expression), single cue representation in red and
blue, respectively.
948
D: Single subject data with superimposed model predictions.
949
950
951
952
953
954
Figure 5. Adaptation and generalization to single pre-movement cue
representations.
955
956
A: Hand-path error of each group adapting to either a CW (blue) or CCW
(red) force field.
957
B: Adaptation Index of both force fields (one group each).
958
959
960
961
C: Generalization around the trained pre-movement direction. The model fits
of single cue representations are superimposed in red and blue, respectively.
Group average data, error bars denote SE. Dashed line shows the net sum of
the two single cue representations.
962
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966
Table 1. ANOVA results of the pre-movement analysis. The pre-movement
was analyzed with respect to dwell time, peak speed and duration. None of
these main factors showed a significant effects and can therefore not explain
our results.
967
968
969
Table 1
Dwell Time
Peak Speed
Duration
Pre-movement
angle
F13,517 = 1.23;
p=0.35
F13,517 = 11.74;
p=0.25
F13,517 = 4.83;
p=0.06
Hand
F1,517 = 0.09;
p=0.81
F1,517 = 0.001;
p=0.97
F1,517 = 0.38;
p=0.63
Trained Hand
F1,517 < 0.001;
p=0.99
F1,517 < 0.001;
p=0.99
F1,517 = 0.04;
p=0.88
Pre-movement
angle x Hand
F13,517 = 1.83;
F13,517 = 0.96;
F13,517 = 1.7;
p=0.04
p=0.49
p=0.06
Pre-movement
angle x Trained
Hand
F13,517 = 10.52;
F13,517 = 0.31;
F13,517 = 0.28;
p<0.001
p=0.99
p=0.99
Hand x Trained
Hand
F1,517 = 10.95;
F1,517 = 11.89;
F1,517 = 7.32;
p=0.001
P<0.001
p=0.007
A
B
Null
Training
Probing
Target
12 cm
-135º
y
Via-Point
-95º
x
cm
}
95º
10
Start
135º
-45º
45º
-45º
45º
0º
C
e.g. Channel
Null
Probing
Untrained
Hand
182
Trained
Hand
Null
Training
Probing & Re-exposure
Wash-Out
182
400
420
70
160
161
NS
NS
NS
NS
Probing Phase
C
1
0.5
0
-0.5
-1
1
0.5
0
-1
-0.5
D
# Exposure
300
1
**
**
**
30
**
IJ= 28.3
**
**
IJ = 77.9
**
Adaptation Phase
Adaptation Phase
**
A
20
10
0
-10
-30
-20
Dominant Hand
30
20
Non - Dominant
Hand
B
10
0
-10
-20
-30
1
Adaptation Index (AI)
Adaptation Index (AI)
Hand-Path Error (cm2)
Hand-Path Error (cm2)
40
NS
CW
CCW
NS
NS
CW
CCW
NS
# Channel
45
Probing
Phase
41
A
B
Dominant Hand (Trained) - Non-Dominant Hand (Transfer)
Non-Dominant Hand (Trained) - Dominant Hand (Transfer)
1
0.8
Adaptation Index (AI)
0.6
R2 = 0.98
R2 = 0.97
R2 = 0.94
R2 = 0.93
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
CW
CCW
-1
-180
-135
-95
-65 -45 -30 -15 0 15 30 45
65
95
135
180
Pre-Movement Direction (deg)
-180
-135
-95
-65 -45 -30 -15 0 15 30 45
65
95
135
180
Pre-Movement Direction (deg)
A
B
**
**
1
NS
20
NS
Adaptation Index (AI)
Hand-Path Error (cm2)
30
10
0
-10
0.5
CW
CCW
0
-0.5
NS
-20
NS
*
**
Adaptation Phase
Probing Phase
1
160
161
Probing
Phase
Adaptation Phase
195
1
40
41
45
# Exposure
D
1
0.8
Adaptation Index (AI)
0.6
0.4
0.2
Different Force Field Strengths - Individual Subjects
Adaptation Index (AI)
Different Force Field Strengths - Across Subjects
1
Adaptation Index (AI)
C
# Channel
1
0
R2=0.93
R2=0.86
R2=0.91
R2=0.88
R2=0.94
R2=0.84
R2=0.91
R2=0.92
-1
0
-0.2
-0.4
R2=0.95
R2=0.96
-0.6
-0.8
-1
0
-1
-180
-135
-95
-65 -45 -30 -15 0 15 30 45
65
95
135
180
Pre-Movement Direction (deg)
-180
0
180
-180
0
180
-180
0
180
-180
0
180
Pre-Movement Direction (deg)
A
B
20
Adaptation Index (AI)
Hand-Path Error (cm2)
1
0
-20
0.5
CW
CCW
0
-0.5
-1
Probing Phase
Adaptation Phase
1
160
Probing
Phase
Adaptation Phase
161
1
230
40
Adaptation Index (AI)
45
# Channel
# Exposure
C
41
1
Local
0.5
Global
0
Global
-0.5
Local
-1
-180
-135
-95
-65
-45
-30
-15
0
15
30
45
65
95
135
180
Pre-Movement Direction (deg)